Some efficient estimators of the domain parameters

We have proposed, under a general probability sampling design, a two-phase sampling procedure, when the size of a domain (small area) is not known, for estimating the domain total, the first phase being exclusively devoted to arriving at a good estimator of the size of the domain and the second phase being designed to deal with the domain estimation. Apart from this, we have, assuming knowledge of the domain size, mooted two generalized direct estimators. These estimators which have been examined from the standpoint of conditional mean square error are shown to acquit themselves quite well. We have undertaken an assessment of performance sensitivity of one of the estimators in the optimal case when it is based on a predetermined value, say, cd* of domain coefficient of variation and have established that it is worth putting premium on the same in the face of broad-ranging deviations from cd*. An illustrative example has been provided to underscore viability and efficacy of the proposed estimators.